• Pottle or not?

    From Timothy Chow@21:1/5 to All on Tue Sep 21 22:19:28 2021
    XGID=-----bE-D-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O O X |
    | X O | | O O |
    | X O | | O O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | X |
    | X | | X |
    | X | | X |
    | O X X | | X O |
    | O X X | | X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 145 O: 135 X-O: 0-0
    Cube: 1
    X to play 51

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sat Sep 25 19:49:29 2021
    XGID=-----bE-D-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O O X |
    | X O | | O O |
    | X O | | O O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | X |
    | X | | X |
    | X | | X |
    | O X X | | X O |
    | O X X | | X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 145 O: 135 X-O: 0-0
    Cube: 1
    X to play 51

    Given that X is behind in the race, I didn't think that Pottling was
    the right idea here. The trouble is that the alternative play 8/2
    is so weak. Take a look at the variant for comparison.

    1. Rollout¹ 24/18 eq:-0.414
    Player: 40.99% (G:4.20% B:0.18%)
    Opponent: 59.01% (G:16.61% B:0.26%)
    Confidence: ±0.012 (-0.426..-0.402) - [100.0%]

    2. Rollout¹ 8/2 eq:-0.527 (-0.113)
    Player: 38.61% (G:5.65% B:0.22%)
    Opponent: 61.39% (G:20.20% B:0.40%)
    Confidence: ±0.013 (-0.539..-0.514) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    -------
    Variant
    -------

    XGID=--A--bE-C-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O O X |
    | X O | | O O |
    | X O | | O O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | X |
    | | | X |
    | X | | X |
    | O X X | | X O |
    | O X X | | X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 139 O: 135 X-O: 0-0
    Cube: 1
    X to play 51

    1. Rollout¹ 6/1 2/1 eq:-0.371
    Player: 41.92% (G:5.96% B:0.21%)
    Opponent: 58.08% (G:16.79% B:0.29%)
    Confidence: ±0.010 (-0.381..-0.360) - [90.4%]

    2. Rollout¹ 24/18 eq:-0.381 (-0.011)
    Player: 41.86% (G:4.45% B:0.19%)
    Opponent: 58.14% (G:16.59% B:0.34%)
    Confidence: ±0.012 (-0.393..-0.369) - [9.6%]

    3. Rollout¹ 8/2 eq:-0.394 (-0.023)
    Player: 41.46% (G:5.70% B:0.22%)
    Opponent: 58.54% (G:17.05% B:0.35%)
    Confidence: ±0.010 (-0.405..-0.384) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From MK@21:1/5 to All on Mon Oct 18 00:50:36 2021
    Pottle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Thu Mar 3 08:03:11 2022
    XGID=---CBCC-A-b-cB-----dAcba--:0:0:1:42:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X | | O X O O O |
    | X | | O O O |
    | | | O O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X X X |
    | O O | | X X X X |
    | O O X | | X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 104 O: 113 X-O: 0-0
    Cube: 1
    X to play 42

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sat Mar 5 07:29:24 2022
    XG 3-ply plays 5/1 3/1.


    XGID=---CBCC-A-b-cB-----dAcba--:0:0:1:42:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X | | O X O O O |
    | X | | O O O |
    | | | O O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X X X |
    | O O | | X X X X |
    | O O X | | X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 104 O: 113 X-O: 0-0
    Cube: 1
    X to play 42

    It's thematic to race when ahead in the race, and O's 2's and 4's
    are duplicated to hit and cover if X plays 20/14. But should X pay
    now or pay later? XG 3-ply plays 5/1 3/1, but the rollout below
    disagrees.

    1. Rollout¹ 20/14 eq:+0.287
    Player: 58.35% (G:9.35% B:0.22%)
    Opponent: 41.65% (G:3.35% B:0.07%)
    Confidence: ±0.008 (+0.279..+0.295) - [100.0%]

    2. Rollout¹ 5/1 3/1 eq:+0.204 (-0.083)
    Player: 55.85% (G:10.37% B:0.13%)
    Opponent: 44.15% (G:4.28% B:0.08%)
    Confidence: ±0.011 (+0.193..+0.215) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Tue Sep 20 08:27:47 2022
    Since ah_clem seems to be currently interested in "Pottle or not"
    problems, here's one to ponder.

    XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | O | | X |
    | O | | X |
    | O X X | | X X |
    | O X X | | X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 140 O: 123 X-O: 0-0
    Cube: 1
    X to play 32

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From ah...Clem@21:1/5 to Timothy Chow on Wed Sep 21 10:52:06 2022
    On 9/20/2022 8:27 AM, Timothy Chow wrote:
    Since ah_clem seems to be currently interested in "Pottle or not"
    problems, here's one to ponder.

    XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

    X:Player 1   O:Player 2
    Score is X:0 O:0. Unlimited Game  +13-14-15-16-17-18------19-20-21-22-23-24-+
     | X           O    |   | O  X  O  O     O |
     | X           O    |   | O     O        O |
     | X                |   | O                |  | X                |   |                  |
     |                  |   |                  |
     |                  |BAR|                  |
     |                  |   |                  |
     | O                |   | X                |  | O                |   | X                |  | O  X        X    |   | X        X       |
     | O  X        X    |   | X        X     O |  +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count  X: 140  O: 123 X-O: 0-0
    Cube: 1
    X to play 32

    My understanding is that Pottling is more favored when ahead or roughly
    even in the race, but when behind it can be better to hang back for more contact.

    X is behind in the race, so perhaps it's better to do something other
    than run the straggler. But, I'm not seeing anything "very constructive"
    so Pottling would be correct according to the letter of the rule. Also,
    with O's homeboard blot getting hit in the outfield gives X lots of counterplay, so I'll Pottle here.

    20/15.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Thu Sep 22 08:05:47 2022
    XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | O | | X |
    | O | | X |
    | O X X | | X X |
    | O X X | | X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 140 O: 123 X-O: 0-0
    Cube: 1
    X to play 32

    As ah_clem said, sometimes being behind in the pip count can be a
    reason not to Pottle. The idea is that if you disengage into a
    pure race then you'll be losing, and Pottling is a step toward
    disengaging. But there are a couple of other factors to take into
    account:

    1. If your straggler is in danger of being attacked, then Pottling
    may be the lesser of two evils.

    2. If you're well positioned to contain the checker (or checkers)
    that your opponent has not yet escaped, then Pottling does not
    really disengage, and may even help, by bringing another checker
    into the containment effort.

    These factors can be difficult to judge. The rollout belows deems
    that anything other than 20/15 is a whopper, but if I shift the
    blot in O's home board by just one pip to the 2pt, then 20/15 is
    tied with 13/11 13/10 (see variant below).

    1. Rollout¹ 20/15 eq:-0.267
    Player: 43.87% (G:6.46% B:0.27%)
    Opponent: 56.13% (G:18.13% B:0.19%)
    Confidence: ±0.010 (-0.277..-0.257) - [100.0%]

    2. Rollout¹ 13/8 eq:-0.369 (-0.102)
    Player: 42.11% (G:7.60% B:0.32%)
    Opponent: 57.89% (G:22.17% B:0.26%)
    Confidence: ±0.010 (-0.379..-0.358) - [0.0%]

    3. Rollout¹ 13/11 13/10 eq:-0.386 (-0.119)
    Player: 42.04% (G:8.68% B:0.39%)
    Opponent: 57.96% (G:25.23% B:0.36%)
    Confidence: ±0.012 (-0.398..-0.374) - [0.0%]

    4. Rollout¹ 6/1* eq:-0.413 (-0.146)
    Player: 40.95% (G:9.86% B:0.35%)
    Opponent: 59.05% (G:24.39% B:0.50%)
    Confidence: ±0.012 (-0.425..-0.401) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    -------
    Variant
    -------

    XGID=-a-B--D-B--BdD---b-cAb-ab-:0:0:1:32:0:0:0:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | O | | X |
    | O | | X |
    | O X X | | X X |
    | O X X | | X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 140 O: 122 X-O: 0-0
    Cube: 1
    X to play 32

    1. Rollout¹ 20/15 eq:-0.304
    Player: 43.20% (G:6.59% B:0.28%)
    Opponent: 56.80% (G:18.73% B:0.18%)
    Confidence: ±0.005 (-0.309..-0.299) - [67.5%]

    2. Rollout¹ 13/11 13/10 eq:-0.306 (-0.002)
    Player: 44.06% (G:10.40% B:0.53%)
    Opponent: 55.94% (G:24.75% B:0.34%)
    Confidence: ±0.006 (-0.312..-0.300) - [32.5%]

    3. Rollout¹ 13/8 eq:-0.317 (-0.013)
    Player: 43.67% (G:8.64% B:0.40%)
    Opponent: 56.33% (G:21.60% B:0.21%)
    Confidence: ±0.005 (-0.322..-0.312) - [0.0%]

    ¹ 5184 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Tue May 23 09:23:56 2023
    XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:41:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O O O | | O O |
    | X O | | O O |
    | X O | | O |
    | | | |
    | | X | |
    | |BAR| |
    | | | X |
    | | | X |
    | X X | | X |
    | O X X | | X O |
    | O X X | | X O O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 139 O: 162 X-O: 0-0
    Cube: 1
    X to play 41

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Thu May 25 09:20:08 2023
    XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:41:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O O O | | O O |
    | X O | | O O |
    | X O | | O |
    | | | |
    | | X | |
    | |BAR| |
    | | | X |
    | | | X |
    | X X | | X |
    | O X X | | X O |
    | O X X | | X O O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 139 O: 162 X-O: 0-0
    Cube: 1
    X to play 41

    Stepping up into a quadruple shot can be the right idea if it is a
    distraction play. But stepping up to the 5pt isn't a distraction play
    because that's the point O wants to make.

    In the variant, I have changed the roll to 52.

    1. Rollout¹ Bar/24 6/2* eq:+0.035
    Player: 51.07% (G:13.29% B:0.52%)
    Opponent: 48.93% (G:13.06% B:0.47%)
    Confidence: ±0.016 (+0.019..+0.051) - [100.0%]

    2. Rollout¹ Bar/20 eq:-0.069 (-0.104)
    Player: 48.57% (G:11.99% B:0.47%)
    Opponent: 51.43% (G:14.62% B:0.42%)
    Confidence: ±0.016 (-0.085..-0.053) - [0.0%]

    3. Rollout¹ Bar/24 7/3 eq:-0.075 (-0.110)
    Player: 48.60% (G:11.84% B:0.47%)
    Opponent: 51.40% (G:14.25% B:0.53%)
    Confidence: ±0.013 (-0.089..-0.062) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.211.pre-release

    -------
    Variant
    -------

    XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:52:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O O O | | O O |
    | X O | | O O |
    | X O | | O |
    | | | |
    | | X | |
    | |BAR| |
    | | | X |
    | | | X |
    | X X | | X |
    | O X X | | X O |
    | O X X | | X O O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 139 O: 162 X-O: 0-0
    Cube: 1
    X to play 52

    1. Rollout¹ Bar/18 eq:+0.041
    Player: 51.23% (G:12.55% B:0.55%)
    Opponent: 48.77% (G:12.78% B:0.43%)
    Confidence: ±0.016 (+0.026..+0.057) - [99.9%]

    2. Rollout¹ Bar/23 13/8 eq:+0.008 (-0.033)
    Player: 49.88% (G:12.86% B:0.51%)
    Opponent: 50.12% (G:11.96% B:0.40%)
    Confidence: ±0.015 (-0.006..+0.023) - [0.1%]

    3. Rollout¹ Bar/23 6/1 eq:-0.052 (-0.094)
    Player: 48.69% (G:12.95% B:0.38%)
    Opponent: 51.31% (G:13.66% B:0.44%)
    Confidence: ±0.016 (-0.068..-0.037) - [0.0%]

    4. Rollout¹ Bar/23 7/2* eq:-0.060 (-0.101)
    Player: 48.33% (G:13.05% B:0.49%)
    Opponent: 51.67% (G:13.95% B:0.45%)
    Confidence: ±0.017 (-0.077..-0.043) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.211.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)